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Question: RE: 'fsolve' unable to solve once 'conjugate' operator comes in

Question:RE: 'fsolve' unable to solve once 'conjugate' operator comes in

pik1432 245 Maple
fsolve
August 10 2020
1

Hello there, 

Here is a set of non-linear equations:

 

> 

restart;
> 

with(LinearAlgebra):
> 

TrainLoad := -10*10^6*(cos(convert(40*degrees, radians))+I*sin(convert(40*degrees, radians)));

-10000000*cos((2/9)*Pi)-(10000000*I)*sin((2/9)*Pi)

 (1)
> 

 

> 

evalf(TrainLoad, 7);

-7660444.-6427876.*I

 (2)
> 

f1n2 := (0.03 + I*0.1515)*Ix[c1] - (0.03 + I*0.1515)*Ix[c2] + 2 * V[at1] - 55*10^3 = 0;

(0.3e-1+.1515*I)*Ix[c1]+(-0.3e-1-.1515*I)*Ix[c2]+2*V[at1]-55000 = 0

 (3)
> 

f3n4 := (1.6 + I*6.24)*Ix[c1] + (1.12 + I*2.64)*Ix[c2] + V[t] - V[at1] = 0;

(1.6+6.24*I)*Ix[c1]+(1.12+2.64*I)*Ix[c2]+V[t]-V[at1] = 0

 (4)
> 

f5n6 := (1.36 + I*4.44)*Ix[c2] + V[at2] - V[t] = 0;

(1.36+4.44*I)*Ix[c2]+V[at2]-V[t] = 0

 (5)
> 

f7n8 := (-1.12 - I*2.64)*Ix[c1] + (-3.92 - I*12.00)*Ix[c2] + V[at2] - V[at1] = 0;

(-1.12-2.64*I)*Ix[c1]+(-3.92-12.00*I)*Ix[c2]+V[at2]-V[at1] = 0

 (6)
> 

f9n10 := V[t] * (Ix[c1] - Ix[c2]) + TrainLoad = 0;

V[t]*(Ix[c1]-Ix[c2])-10000000*cos((2/9)*Pi)-(10000000*I)*sin((2/9)*Pi) = 0

 (7)
> 

polynomials := {f1n2, f3n4, f5n6, f7n8, f9n10};

{(1.36+4.44*I)*Ix[c2]+V[at2]-V[t] = 0, V[t]*(Ix[c1]-Ix[c2])-10000000*cos((2/9)*Pi)-(10000000*I)*sin((2/9)*Pi) = 0, (-1.12-2.64*I)*Ix[c1]+(-3.92-12.00*I)*Ix[c2]+V[at2]-V[at1] = 0, (0.3e-1+.1515*I)*Ix[c1]+(-0.3e-1-.1515*I)*Ix[c2]+2*V[at1]-55000 = 0, (1.6+6.24*I)*Ix[c1]+(1.12+2.64*I)*Ix[c2]+V[t]-V[at1] = 0}

 (8)
> 

variables := {Ix[c1], Ix[c2], V[at1], V[at2], V[t]};

{Ix[c1], Ix[c2], V[at1], V[at2], V[t]}

 (9)
> 

fsolve(polynomials, variables, complex);

{Ix[c1] = 955.2297105-5281.491898*I, Ix[c2] = -505.0156845+2424.830843*I, V[at1] = 26894.34238+4.981252431*I, V[at2] = 10829.70666+56.66545127*I, V[t] = -623.3636109+1112.165758*I}

 (10)
> 

 

> 

 


The 'fsolve()' command was able to come up with a solution. 

Then, when 'f9n10 := V[t] * (Ix[c1] - Ix[c2]) + TrainLoad = 0;' becomes 'f9n10 := V[t] * conjugate(Ix[c1] - Ix[c2]) + TrainLoad = 0;', 

the command ('fsolve()') refused to produce a solution. 

Would you tell me how to make the 'fsolve()' command work with the 'conjugate()' operator?

Thank you, 

In Kwon Park


 

 

Download no_conjugate.mw

 
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